University of Genoa
PMAR Robotics

Second International Summer School

Screw-Theory Based Methods in Robotics

July 26 - August 6, 2010
Shanghai Jiao Tong University, Shanghai, China

Shanghai Jiao Tong University


Chinese version











The applications of the theory of screws are based on the combined representation of angular and linear velocity, or similarly force and moment, as one element of a six-dimensional vector space.

The importance of screw theory in robotics is widely recognised, in principle. In practice, almost nowhere is it taught to mechanical-engineering students and few know how to use it. Yet, in a variety of areas of robotics, methods and formalisms based on the use of screw geometry and algebra have shown to be superior to other techniques and have led to significant advances. These include the development of fast and efficient dynamics algorithms, discoveries in the nature of robot compliance and mechanism singularity, and the invention of numerous parallel mechanisms.

The instructors in the summer school are the authors of many of these results. They will teach the participants to apply existing techniques and to develop new ones in their own research. The basic theoretical notions will be introduced in a rigorous manner, but the emphasis will be on applications, with examples and exercises.



The school is intended for graduate students and young researchers in robotics. Participants are expected from both academia and industry.

It is strongly recommended that attendees have their own portable computers, preferably with Matlab and Maple. Alternative equivalent software can also be used.

Some experience with (and availability of) 3D CAD software would be helpful but not required.

Software and computer access can be provided to a limited number of participants upon request.



You can download the Tentative Program here.

The material addresses subjects sufficiently fundamental to be within the desirable competence of any mechanical roboticist, and in each area advanced screw-theory based methods have been used to great advantage.

Basic vector-space properties of twists and wrenches: physical interpretation of the linear operations; linear dependence and independence, subspaces; bases and coordinates. (Lecturer: Dimiter Zlatanov)

Scalar products, dual spaces, reciprocity. Constraint and freedom in mechanisms. Constraint analysis. Type synthesis of single-loop mechanisms and parallel manipulators. (Lecturers: Xianwen Kong and Dimiter Zlatanov)

Velocity and singularity analysis of parallel and interconnected-chain mechanisms. Derivation of input-output velocity equations and singularity conditions. (Lecturers: Matteo Zoppi and Dimiter Zlatanov)
Mappings between screw spaces, stiffness and inertia. Structure of robot compliance. Eigenvalue problems and eigenscrews. Synthesis with springs. (Lecturer: Harvey Lipkin)
6D formulation of the dynamics of individual rigid bodies and rigid-body systems. Equations of motion. Dynamics algorithms. (Lecturer: Roy Featherstone)
Basic Lie group theory, matrix representations of the group of rigid-body displacements.Lie algebras as related to screw theory. The exponential map andits applications in modern robotics (Lecturer: Jon Selig).


Special Lecture

This year Summer Screws includes a special lecture on design.

Topic: The GF set of basic motion units. Boolean calculation of the GF set. Type Synthesis of chain and parallel mechanisms.

Lecturer: Feng Gao



Dimiter Zlatanov has used screw theory in the singularity and mobility analysis of mechanisms. He is the inventor of one of the first-known 4-dof parallel mechanisms and has presented courses and talks on screw-based methods in various universities.

Xianwen Kong is the inventor of numerous parallel mechanisms and the co-author of the book Type synthesis of parallel mechanisms. His results have been based on methods from screw-system theory.

Matteo Zoppi has developed screw-theoretical techniques for the derivation and application of velocity equations for complex-chain manipulators. He is also the inventor of a number of mechanisms.

Harvey Lipkin has worked more than any one on applying screw-theoretical methods in different areas of robotics and mechanisms, such as hybrid control, compliance, vibrations, and dynamics. He has taught various aspects of screw theory and supervised graduate students in the use of such methods.

Roy Featherstone is the inventor of the Articulated-Body Dynamics Algorithm, and the author of the books Robot Dynamics Algorithms and Rigid Body Dynamics Algorithms. His ground-breaking work in dynamics has relied on a screw-theoretical formalism for the formulation of the equations of motion.

Jon Selig is the foremost specialist on advanced geometrical and group-theoretical methods in robotics. He is the author of the book Geometric Fundamentals of Robotics, and several book chapters on the application of Clifford algebras and Lie group theory. He edited and co-authored the collection Geometrical Foundations of Robotics.

Feng Gao is the foremost specialist on the design and application of parallel robotics in China. He is the inventor of more than 30 patents related to various parallel mechanisms and parallel robotic devices. He is associate editors of Transaction of ASME Journal of Mechanism and Robotics and IFToMM Mechanism and Machine Theory.


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